0004.ptx

<exercise masterit-seed="1999" masterit-slug="C4" masterit-name="Homogeneous second-order linear IVP">
  <statement>
    <p>Explain how to find the particular solution to each given IVP.</p>
    <ol>
      <li>
        <me> {x''} - 2 \, {x'} = 3 \, {x} \hspace{2em}
           {x} (0)= -1 ,
           {x} '(0)= -19 </me>
      </li>
      <li>
        <me> 0 = -25 \, {y} - {y''} \hspace{2em}
           {y} (0)= -4 ,
           {y} '(0)= 5 </me>
      </li>
    </ol>
  </statement>
  <answer>
    <me> {x} = -5 \, e^{\left(3 \, t\right)} + 4 \, e^{\left(-t\right)} </me>
    <me> {y} = -4 \, \cos\left(5 \, t\right) + \sin\left(5 \, t\right) </me>
  </answer>
</exercise>